"A miracle occurs when the world is not left to itself, when something distinct from the natural order as a whole intrudes into it."  This is Mackie's definition.  It is more honest than Christian definitions which pretend to know exactly what is supposed to be doing them.  People prefer his definition to Hume's which called a miracle a violation of nature.  Yet “A miracle occurs when the world is not left to itself, when something distinct from the natural order as a whole WORKS on it" is even more preferable.  Intrudes implies something like an invasion as if the supernatural and nature ban each other and that is controversial.  Dropping the idea of intrude avoids the argument that nature cannot do miracles therefore they do not happen which is only true if there really is no supernatural.  But the supernatural is the question we need to examine.  We need to think about it undogmatically.

According to religion, miracle such as Jesus returning from the dead to teach things can be a direct sign or can only make sense in a specific religious context.  In the latter case it is indirect.  The apparitions of Lourdes fit into the Catholic system of religious doctrine and morals but not Mormonism even though the vision does not say, "The Catholic Church is true." It does not have to.

The assumption that miracles and wonders are signs denies the statements of those such as Dion Fortune in Sane Occultism that "There is no correlation between occult powers and spirituality."  In other words, such abilities do not depend on how good or trustworthy you are.  If miracles are signs that is really saying the messenger is reliable and good.  It ends up being about the person not what they do.

The Roman Catholic Church using its claimed infallibility at Vatican I, Session 3, The Dogmatic Constitution on the Catholic Faith, Chapter 3, “On Faith,” declared:

Canon 3 - If anyone says that divine revelation cannot be made credible by external signs, and that therefore men and women ought to be moved to faith only by each one’s internal experience or private inspiration: let him be anathema.

Canon 4 - If anyone says that all miracles are impossible, and that therefore all reports of them, even those contained in sacred scripture, are to be set aside as fables or myths; or that miracles can never be known with certainty, nor can the divine origin of the Christian religion be proved from them: let him be anathema.

From http://www.newadvent.org/cathen/10338a.htm -

The word semeion means "sign", an appeal to intelligence, and expresses the purpose or final cause of the miracle. A miracle is a factor in the Providence of God over men. Hence the glory of God and the good of men are the primary or supreme ends of every miracle. This is clearly expressed by Christ in the raising of Lazarus (John 11), and the Evangelist says that Jesus, in working His first miracle at Cana, "manifested his glory" (John 2:11). Therefore the miracle must be worthy the holiness, goodness, and justice of God, and conducive to the true good of men. Hence they are not performed by God to repair physical defects in His creation, nor are they intended to produce, nor do they produce, disorder or discord; do they contain any element which is wicked, ridiculous, useless, or unmeaning. Hence they are not on the same plane with mere wonders, tricks works of ingenuity, or magic. The efficacy, usefulness, purpose of the work and the manner of performing it clearly show that it must be ascribed to Divine power. This high standing and dignity of the miracle is shown, e.g., in the miracles of Moses (Exodus 7-10), of Elias (1 Kings 18:21-38), of Eliseus (2 Kings 5). The multitudes glorified God at the cure of the paralytic (Matthew 9:8), of the blind man (Luke 18:43), at the miracles of Christ in general (Matthew 15:31, Luke 19:37), as at the cure of the lame man by St. Peter (Acts 4:21). Hence miracles are signs of the supernatural world and our connection with it.
A miracle is what is not naturally possible. It is a supernatural occurrence. It is paranormal.

Religion says that God needs to tell us things we do not know and cannot know so he uses miracles to reveal the truth to us.  Miracles then teach us.  But what always happens is the miracle teaches one or two people and they teach other people.  So all that happens is a claim is made that gives them authority to teach others.  It is clear why that is a very dodgy way to go about things.  If a miracle is about teaching all need to be taught by it.  And if that is bad having people have to listen to what others say a miracle taught them is worse.  As J L Mackie wrote, "the point at issue is, whether a miracle has occurred which would enhance the authority of a specific sect or teacher."  Faith in divine revelation does not exist.  What you have is faith in the honesty and rightness of the men who say they got the truth through a miracle.
Even if you do not believe in the supernatural, some things cannot be explained. Believers in miracles may assume that some of these things are miracles. Something being unexplained or unexplainable does not entitle you to assume a miracle has happened. If a miracle is a sign then it is a sign that you are entitled. But that is a lie. You are not. Regard the miracle as a lie if it pretends to be a sign or otherwise regard it as a mere random fluke and not a sign.

Christians pretend that they regard miracles as evidences of God’s action in the world and that God does them to provide evidence to attract us to his Church and to believe what it believes.

This view is sectarian through and through. It is intrinsically bigoted and about using doctrine to cause division and arrogance wherein members of a religion will consider themselves superior to members of another and seek to rival it. What is wrong with it? If there is a God, we should be getting to know him through a relationship with him. But the notion that God wants us merely to accept truths about him implies he is keeping distant from us. The true Christian if he exists has a relationship with God and not with the words about God or the doctrines about God or the books or Bibles about God. Knowing Annie is a nice person is no good. You need to bond and relate with her. And so it is with God. While a relationship with God will help us see the truths about him, it does not follow that the relationship is merely about doctrine. If it were it would not be a relationship. If miracles are signs, they are not signs from God. It is outrageous that people will flock to miracle sites instead of trying to relate to God in their hearts.

Miracle believers sometimes say that miracles are real but add that they don't know which ones are real or not. They say many of the miracle testimonies might be based on wishful thinking. This is a fair point because only witnesses can know or should know if the miracles are convincing or if wishful thinking played a role. This means you cannot depend on miracles as signs when you don't know for sure what miracles really are miracles! It would mean you do not believe miracles can happen or are real but are only guessing it.

The teaching that faith in God or the knowledge of God is to be a relational matter implies that those who do not believe are deliberately darkening their minds and hearts. In Romans 1 Paul states that creation shows what God is like. It shows his nature. Romans 1 is about what God has shown everybody in general of his nature. It is not about nature showing the existence of God. To accuse people who do not believe in the Christian or Jewish version of God of acting in bad faith is vile sectarian arrogance. Augustine and Calvin argued that the knowledge of what God is like is innate. They followed the teaching of Romans 1 where idolaters are not condemned for thinking there is no God but for seeing what he is like and ignoring it. Paul in Romans 1:28 says the idolaters did not see fit to recognise God meaning it was their own fault. Verse 25 says that idolatry is simply preferring what you want to believe about the divine to the actual truth.

Jesus himself said in Luke 16:31 that if people will not believe the call to repentance made in the bible word of God that a man rising from the dead to tell them to repent will not do them any good. He implied that any miracles would be useless. Imagine then how useless Catholic miracles are as signs for the Catholics state that you do not have to believe in them and you can be a good Catholic and debunk them.

Natural theology insists that God has given us the rational powers to work out that he probably exists and that we should have a relationship with him. Christians object that it leaves us to find God rather than God finding us. But our thinking ability and ability to think about evidence could be interpreted as a gift or grace from God. It could be thought that he guides it. Evidence is a gift from God if there is a loving God.  Us finding God does not mean God is left out deliberately or that he is not there.  The argument is really based on trying

Miracles demand natural theology in the sense that you have to reason from miracles to the existence of God. Miracles seem pointless for if God helps our reasoning then we should not need them but find nature to indicate the existence of God. Religion complains that natural theology tends to be too optimistic about the human power to learn of the probability of God and to prepare for relating to him. It is too optimistic then about human nature. But surely it is better to listen to reason than to feelings or to what we think we experience in terms of a relationship with God? If reason has dangers the others have bigger dangers. Christians say natural theology is about finding God without his aid and thus it is arrogant. But there is more arrogance in believing in God because you think he is inspiring you than in you trying to find out about him with your unaided powers. If we have to work out God's existence from his miracles and do it without his aid, then that is just natural theology we are doing. If it is bad then miracles are bad.

The Bible insistence that we must live by faith and not by sight (2 Corinthians 5:7) tells us not to seek wonders or grand experiences of God and says that anything based on anything other than pure trust in Jesus is a sin.

God, if wholly good and wholly powerful, does not do miracles to fix things he has got wrong. He does them as signs of his love and presence and to teach us and inspire us. Religion says that God being almighty does not make mistakes so miracles, changing the way nature works say by making the Virgin Mary appear, are done to make people see what the true religion is. God doesn’t need to do miracles except as signs. So a miracle can only happen because God is desperate and at the end of his tether to get people to believe and convert. But the very fact that he needs miracles to persuade people shows that he does make mistakes. If he had organised the spread of the word of God better and made people brighter and more interested, just by giving us the same brain faculties that very religious people have that cause their religiosity, when it comes to religion more than anything else there would be no need for the miracles for after all the faith has to make sense and be the most credible faith on earth for otherwise all the miracles of the day are of no assistance.

Religion uses miracles as evidence for the truth of its claims. If a miracle happens in a religion it is said that it is intended by God to indicate that the religion is his one true religion. Others argue that God can do a miracle in any religion for the miracle is about confirming the truths in that religion which is not the same thing as saying the religion is the only true religion. It could be argued that the apparition of Our Lady of Lourdes only verifies the Catholic devotion to Mary and the rosary and the sinlessness of Mary but not the Catholic faith as a whole. This view is unpopular for it leads to confusion among believers. It would make more sense for God to use miracles to promote the religion that teaches the truth faithfully and without error rather than specific doctrines as such.

Miracles should be rare. If a miracles are signs from God, then only one good and well-attested sign is necessary. God doing more signs would imply that God has a lack of confidence. People are comforted by miracles and that is strange for they imply that if there is a God then he is a bungler.

A miracle cannot prove God's existence unless a non-miracle does it too. Think of it this way. You have to believe that nature works a certain way - eg stones don't come to life - in order to recognise a miracle - the temporary change in the way it works. So unless you see non-miracles as the work of God you cannot see the miracle as the work of God. It follows then that a miracle is useless as propaganda. A miracle does nothing to show that God exists any more than a non-miracle does. So the miracle is pointless. No decent God will manipulate our stupidity and desire for religious thrills by doing miracles to convert us for they only make us worse.

Religion says that miracles are a sign that its doctrines are true. For example, in Catholicism it is said that God does miracles to draw people to the Catholic faith, the one true faith. People have a liking for believing in magic. That is the attraction. They like to be astonished. How the Church can say miracles are signs when miracle fans and pilgrims to miracle sites will respond to them superstitiously shows it finds no shame in lying outright. Miracles imply approval for superstition.

Not all miracles claim to be signs. Miracles such as blood oozing from communion wafers are not edifying but disgusting and sinister and shocking.

Why would God heal people miraculously at Lourdes to show that Mary appeared there? The miracle itself and the meaning are often disputed. God should only do miracles that verbally communicate a message. That makes things clearer.

The Church says it regards miracles as signs from God and that it believes he uses them to teach us some truths. It does not believe that for it makes up its mind first and then looks for miracles that seem to support what it wants to believe. If God goes along with that then miracles are not signs. Many forms of religion use miracles as evidence for the truth of their claims. Miracles are not evidence for religion being true or for the existence of God. Why? Because we don’t really know what they are evidence for - if anything!

If miracles are meant to convert us to what religion calls the truth, its teachings, then why do we just do and think what will gratify us? We do not believe in anything unless we get pleasure from it so God should change our feelings to get us to accept doctrines for we can’t help them anyway if he wants us to believe. Miracles deny that there is a God for they speak of supernatural incompetence.
If miracles are signs telling us what doctrines are true or approved by God, it follows then that if miracles are signs we should look to see if the doctrines they bolster are true. THEN we should check if the miracles are real and verify them. This is never done.
What religion is doing is this, "Miracles show us the faith is true" which translates as, "Miracles show us the faith is true and the faith is true for miracles say so." That is a totally irrational vicious circle.
Philosophers say that if miracles happen they must be done for some good purpose and as signs to draw people to the truth. But the Bible contradicts this with silly unnecessary miracles taking place. E.g.: Balaam’s donkey speaking. And if that is not bad enough the Catholic Church tells us that Jesus' mother appeared at Lourdes a number of times and gave no message and just kept Bernadette looking at her.
Miracles do not square with the view that God does good just because he is good. They do not make much of an effort to show goodness directly. For example, is it really good for John to be instantly cured of cancer when he might take a worse illness later? What good does putting stigmata wounds on Padre Pio do? The goodness must be shown clearly and directly and in such a way that nobody can deny the obvious goodness. Instead we get miracle reports and Christians are forced to speculate about in what way they show short-term and long-term good. And nobody agrees on what the goodness is. It's rationalisation.
The evidence we look for is the evidence for the direct goodness in the miracle. The case for it being supernatural should come second. If miracles are really about God giving us good example and edifying us that is the way it has to be. Religion cares about supporting the view that the miracles are supernatural or proving the miracles supernatural. And even then, it is only some of the alleged miracles that suit its claims that it is the true religion that it wants to check.
Christians and Muslims and Jews claim that they are systems of faith. They claim that those who dispute their claims are also depending on faith. Which faith then is the most reasonable? The one that refuses to easily believe in miracles, secularism. Because if these are all different systems of faith then it follows that the one that suits our experience best is the reasonable one. When nature goes on its normal way and cows don’t give birth to pigs and statues don’t bleed it follows that we should believe in secularism for all forms of faith cannot be equally reasonable or good.